Stir the Oreo cookie crumbs with the melted butter in a bowl until the crumbs look evenly damp, like wet sand. When you pinch some in your fingers, it should clump lightly instead of falling apart.

Pour the crumb mixture into an 8–9 inch springform pan. Press it firmly across the base and slightly up the sides with your fingers or the bottom of a glass. The surface should look even, with no loose crumbs sliding around. Set the pan in the fridge while you make the filling.

In a large bowl, beat the softened cream cheese and sugar with an electric mixer on medium speed until smooth and creamy, with no lumps. Scrape down the bowl. Add the hot chocolate mix and keep beating until the mixture looks uniform and you no longer feel any grit when you rub a bit between your fingers.

Mix in the peppermint extract a little at a time, beating briefly and tasting as you go. You want it to taste like peppermint hot chocolate, cool on the tongue without feeling sharp.

Pour 2 cups of heavy whipping cream into the bowl with the cream cheese mixture. Start the mixer on low, then move to medium. The filling will look loose at first, then thicken. Stop when it is fluffy and forms soft peaks that curl over when you lift the beaters.

Take the pan from the fridge and pour the peppermint cheesecake filling over the chilled crust. Smooth the top with a spatula so it is level and reaches the edges. Tap the pan lightly on the counter to release any air bubbles.

Cover the pan lightly with plastic wrap and refrigerate for at least 6 hours, or freeze for about 4 hours if you need it firmer. The center should have a gentle jiggle, not a loose wobble, when you move the pan.

Close to serving time, beat 2 cups heavy cream with powdered sugar and peppermint extract in a cold bowl. Start on low, then go to medium-high until the cream holds soft to medium peaks that look smooth.

Spread or pipe the whipped cream over the chilled cheesecake. Garnish with mini marshmallows, crushed peppermints, and chocolate shavings so each slice gets a bit of everything.

Run a thin knife around the edge of the pan, release the springform ring, and slice with a long knife dipped in hot water and wiped dry between cuts. Serve cold.